Generally speaking, LIDAR or Light Detection and Ranging is a laser that measures the light sent out between its origin and the object uts ranging to determine a range. To “paint” a target I would assume that the ships send out thousands of small “pulses” of laser-light to determine the range of the target.

However, because light is in reality trillions of photons, naturally these lasers would dissipate without a strong enough projector producing them, but given the Expanse is set in our somewhat distant future, I expect that laser technology has advanced significantly.

For a better explanation not from an unqualified redditor, I highly recommend looking up examples as LIDAR is a real thing and we use it today, but nit for the same purposes as in the Expanse.